English

A Reifenberg type characterization for $m$-dimensional $C^1$-submanifolds of $\mathbb R^n$

Differential Geometry 2018-04-17 v2

Abstract

We provide a Reifenberg type characterization for mm-dimensional C1C^1-submanifolds of Rn\mathbb R^n. This characterization is also equivalent to Reifenberg-flatness with vanishing constant combined with suitably converging approximating mm-planes. Moreover, a sufficient condition can be given by the finiteness of the integral of the quotient of θ(r)\theta(r)-numbers and the scale rr, and examples are presented to show that this last condition is not necessary.

Keywords

Cite

@article{arxiv.1804.02187,
  title  = {A Reifenberg type characterization for $m$-dimensional $C^1$-submanifolds of $\mathbb R^n$},
  author = {Bastian Käfer},
  journal= {arXiv preprint arXiv:1804.02187},
  year   = {2018}
}